|1/2-1|+|1/2-1/3|+|1/3-1/4|+.+|1/99-1/98|+|1/100-1/99|
=1-1/2+1/2-1/3+1/3-1/4+.+1/98-1/99+1/99-1/100
=1-1/100
=99/100